An approximation algorithm for K-best enumeration of minimal connected edge dominating sets with cardinality constraints

K-best enumeration, which asks to output k-best solutions without duplication, is a helpful tool in data analysis for many fields. In such fields, graphs typically represent data. Thus subgraph enumeration has been paid much attention to such fields. However, k-best enumeration tends to be intractab...

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Vydáno v:Theoretical computer science Ročník 1005; s. 114628
Hlavní autoři: Kurita, Kazuhiro, Wasa, Kunihiro
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 24.07.2024
Témata:
Approximate algorithm
Connected edge dominating set
K-best enumeration
Output-sensitive enumeration
Output-sensitive enumeration
Connected edge dominating set
Approximate algorithm
K-best enumeration
ISSN:0304-3975, 1879-2294
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Shrnutí:K-best enumeration, which asks to output k-best solutions without duplication, is a helpful tool in data analysis for many fields. In such fields, graphs typically represent data. Thus subgraph enumeration has been paid much attention to such fields. However, k-best enumeration tends to be intractable since, in many cases, finding one optimum solution is NP-hard. To overcome this difficulty, we combine k-best enumeration with a concept of enumeration algorithms called approximation enumeration algorithms. As a main result, we propose a 4-approximation algorithm for minimal connected edge dominating sets which outputs k minimal solutions with cardinality at most 4⋅OPT‾, where OPT‾ is the cardinality of a minimum solution which is not outputted by the algorithm. Our proposed algorithm runs in O(nm2Δ) delay, where n, m, Δ are the number of vertices, the number of edges, and the maximum degree of an input graph.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114628